Physics Question?

Question

Hoover Dam was built in the 1930s to provide electricity for the southwest U.S. and to prevent the wild Colorado River from flooding. Hoover Dam is about 380 m wide and is about 221 m high. Assume that Hoover Dam can be approximated by slab geometry with a width of 380 m (W). What is the total force (newtons) on the dam face if the water level from Lake Mead (holding basin for Hoover Dam) is 200 m (D)? Assume the density of water in Lake Mead is 1000 kg/m3.

Answer 1

The pressure increases as you go down. To get the total force on the entire face of the wall, you need an average of pressure over the entire wall. Well you could also get involved with calculus but I wouldn't unless I absolutely had to.

How to do that. --- Consider a point halfway down the face, measure the pressure, then measure pressure 1 meter above halfway, repeat 1 meter below halfway. Take the 2nd and 3rd reading and average them. You will get the same as the 1st reading. For this question, you can use the average pressure applied to the entire face.

You can get pressure at the halfway point with the formula
p = rho*g*h
where rho is the density, g = 9.8 m/s^2, and h is 1/2 the total depth.

And then total force is average pressure*total area.